On April 21st 2015, Google started taking into account the mobile-friendliness of websites when determining mobile search engine results. This is so Google can make it easier for people using mobile devices to access websites that have been optimised for mobile usage.
Google offers tools to help you understand how well your site is optimised for mobile devices. You can test each of your website's pages for mobile-friendliness here.
Google will be inspecting several page elements for mobile optimisation. These include:
Can your text be easily read on a mobile device? The user should not have to zoom in or out in order to read the text on the page. There shouldn't be any need to scroll horizontally.
Buttons should be easy to touch and well spaced out. Your buttons shouldn't be so close together that there is a risk of pressing two buttons simultaneously.
Does your site rely on Flash? Flash may not be available on some mobile devices, leaving users frustrated. Additionally, do not use pop-ups - they can be difficult to close on mobile devices, leading to a higher bounce rate.
Do your pages load too slowly? The longer your pages take to load, the higher the chance of your visitors leaving prematurely. Users are increasingly less likely to wait for pages to load, so the faster the better.
Are there any links to pages that have not been optimised for mobile usage? When users click a link on the mobile version of the site but are taken to a page that has not been made mobile-friendly, this can disrupt their navigation of your website and cause them to leave the site.
Are your titles and descriptions as concise as possible? Because there's less screen space available, try to keep your titles, meta descriptions and URLs as short as possible. However, you should still try to maintain the quality of the information within them as much as you can.
More information on SEO best practices can be found in this PDF from Google.
Even after you have optimised your site, it's important to periodically reassess your pages and make sure you keep them operating at their best. Best practices do change and you need to keep your websites up to date and mobile-friendly.